Dispersivity is actually a factor which represents our " lack of information " about the system we are simulating.
The models require input of soil characteristics like the relations between variable unsaturated soil moisture content, water tension, water retention curve, unsaturated hydraulic conductivity, dispersivity and hydrological phenomena.
There are many small details about the aquifer which are being averaged when using a macroscopic approach ( e . g ., tiny beds of gravel and clay in sand aquifers ), they manifest themselves as an " apparent " dispersivity.
Because of this, ? is often claimed to be dependent on the length scale of the problem the dispersivity found for transport through 1 m 3 of aquifer is different from that for transport through 1 cm 3 of the same aquifer material.